There are several metres of space above the cockpit, forward of the upper passenger deck of the A380. I know some of it is taken up by the stairs, but what is the rest used for? Avionics and electrical systems are my guesses. Looking forward to hearing from the experts on here!

Correct, the upper avionics bay is there, with an entrance from the cabin (the top of the main stairway, on the right side)
The Flight Crew Rest Compartment is also stuck in there, between the main cabin and the cockpit itself.

My goal as an engineer is to fill my soul with coffee and become immortal

Is it even certified to have passenger accommodation on the cargo deck as shown there? Or a passenger lift for that matter?

Entire top deck first class make it definite Fantasy Air no matter what, if there was that kind of F load to be had on a route we'd probably see every airline in the world trying to serve it multiple times a day with smaller planes...

I believe the answer is: Nothing. Emirates has showers here. I'm sure that'll keep going until the first time they hit turbulence and someone gets their skull impaled on the shower head. In the mean time, most airlines seem to use the space to carry extra air. Or... ?pictures? in Air France's case...

Quoting 747-600X (Reply 14):In the mean time, most airlines seem to use the space to carry extra air. Or... ?pictures? in Air France's case...

I thought these 'areas' were situated at the rear of the upper deck? I agree with you that they are wasted space, especially the Air France gallery. I think they need a few more furnishings to be a small lounge.

This is how it looks in this compartment, it is the room for the aircond drum mixer (this was probably the only correct things in the first cutaway ), where the recirculating air from the cabins is mixed with the fresh air from the air cond pacs in the wingroots, Tom calls it the snakepit , good name: